Data driven modeling and stability analysis for stochastic interconnected systems with uncertainties

This paper proposes a deep neural network (DNN)-augmented inverse optimal adaptive control for stabilizing stochastic interconnected systems, focusing on challenges posed by unmodeled dynamics and uncertainties. A structured small-gain framework is developed to address the mutual dependencies among interconnected subsystems and to ensure the input-to-state practical stability in probability. To approximate unmodeled nonlinearities, a DNN-based identifier is integrated into each subsystem, allowing real-time estimation of uncertain dynamics while preserving the analytical tractability of the controller. Through this idea, we develop an adaptive controller that guarantees uniform boundedness of the interconnected system and ensures state convergence within a small neighborhood of the origin while optimizing overall system performance. Finally, an automobile suspension system is presented to demonstrate how the proposed approach effectively achieves closed-loop stability for stochastic interconnected systems while incorporating inverse optimal control design.